Remark on the Statistical Significance of Flares in Poisson Count Data

When is an X-ray flare (i.e., a count excess in a certain interval of time-varying Poisson data) statistically significant? First, the answer depends crucially on the time variation of the source (e.g., Cyg X-1) on time scales much longer than that of the supposed flare: "small," "slow" variations dramatically increase the probability of spurious "short," "large" flares. Second, the probability of spurious flares extending over manytime bins is further enhanced by the fact that their position and duration are specified only post hoc in examining the data. We give quantitative calculations of these two effects. Subject heading: X-rays